Séminaire Lotharingien de Combinatoire, 93B.91 (2025), 12 pp.
Raj Gandhi and Gabe Udell
A Degeneration of the Brick Variety and a Mixed Subdivision of the Associahedron into Cubes
Abstract.
We study a degeneration of Escobar's brick variety in cases where it is toric. We show that the components of the central fibre of the degeneration are reduced toric products of Richardson varieties. We write the moment polytope of the variety, which has the same normal fan as the brick polytope of Pilaud and Santos, as a Minkowski sum of Bruhat interval polytopes and show that the polyhedral subdivision induced by the degeneration is a mixed subdivision. As corollaries, we obtain a characterization of toric Richardsons, and a subdivision of the associahedron into combinatorial cubes.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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